The mind-bending thing about it is thus: there are an infinite multitude of “you” throughout the multiverse expressing every “you” that could, or even could not, be. However, there are infinitely more realities with no “you” at all. The set of infinities containing an expression of “you” is necessarily smaller than the set of infinities that do not contain an expression of “you” simply owing to the very narrow nature of eventualities required to express “you” into existence. In point of fact, that set if infinitesimal labeled “you” is infinitesimal in comparison to the set labeled “not you”, and yet still uncountable in its infinity.
I’m not sure how sound that reasoning is, it’s difficult to use intuition to determine whether one infinite set is bigger than another. Infinity is weird.
Say for instance you have two infinite sets: a set of all positive integers (1, 2, 3…) and a set of all positive multiples of 5 (5, 10, 15…). Intuitively you might assume the first set is bigger, after all it has five times as many values, right? But that’s not actually the case, both sets are actually exactly the same size. If you take the first set and multiply every value by 5 you have the second set, no need to add or remove any values. Likewise, dividing every value in the second set gives you the first set again. There is no value in one set that can’t be directly mapped to a unique value in the other, therefore both sets must be the same size. Pick any random number and it’s 5 times as likely to be in the first set than the second, but there are not 5 times as many values in the first set.
With infinitely many universes one particular state being a few times more or less likely doesn’t necessarily matter, there can still be as many universes with you as without.
The ultimate conceit is that infinities are a wonderfully engaging concept, but truly comprehending them as a tangible thing is inherently futile. We want to make these comparisons. They do, in some ways, hold some kind of meaningful as a concept, because we like one thing to be bigger or better than the other. But, at the scale of infinity, these comparisons are arbitrary and largely meaningless in any practical way.
Where it gets strange is that there are actually an equal number of multiverse that have a version of you as there are that do not contain a version of you.
For the sake of simple math, let’s assume that there are an infinite number of multiverses and that the amount of those which contain a version of you is 1/10th.
So let’s take the amount of multiverses and divide them by ten. What do we get? Infinity.
It’s like trying to say there are fewer rational numbers between 1 and 2 than there are between 2 and 10. The number is always infinite.
No, there are some infinities bigger than other infinities. I know it sounds dumb, but this has been mathematically demonstrated. All infinities aren’t the same size, basically.
The set of rational numbers is larger than the set of integer numbers, even though they are both infinite.
What the person you replied is trying to say is that the intinite amount of universes that exist is infinitely larger that the infinite amount of universes in which you exist.
Personally, I think we can’t mathematically understand if the multiverse is a countable or uncountable infinite… Maybe we can? I don’t know.
The mind-bending thing about it is thus: there are an infinite multitude of “you” throughout the multiverse expressing every “you” that could, or even could not, be. However, there are infinitely more realities with no “you” at all. The set of infinities containing an expression of “you” is necessarily smaller than the set of infinities that do not contain an expression of “you” simply owing to the very narrow nature of eventualities required to express “you” into existence. In point of fact, that set if infinitesimal labeled “you” is infinitesimal in comparison to the set labeled “not you”, and yet still uncountable in its infinity.
I’m not sure how sound that reasoning is, it’s difficult to use intuition to determine whether one infinite set is bigger than another. Infinity is weird.
Say for instance you have two infinite sets: a set of all positive integers (1, 2, 3…) and a set of all positive multiples of 5 (5, 10, 15…). Intuitively you might assume the first set is bigger, after all it has five times as many values, right? But that’s not actually the case, both sets are actually exactly the same size. If you take the first set and multiply every value by 5 you have the second set, no need to add or remove any values. Likewise, dividing every value in the second set gives you the first set again. There is no value in one set that can’t be directly mapped to a unique value in the other, therefore both sets must be the same size. Pick any random number and it’s 5 times as likely to be in the first set than the second, but there are not 5 times as many values in the first set.
With infinitely many universes one particular state being a few times more or less likely doesn’t necessarily matter, there can still be as many universes with you as without.
The ultimate conceit is that infinities are a wonderfully engaging concept, but truly comprehending them as a tangible thing is inherently futile. We want to make these comparisons. They do, in some ways, hold some kind of meaningful as a concept, because we like one thing to be bigger or better than the other. But, at the scale of infinity, these comparisons are arbitrary and largely meaningless in any practical way.
Don’t worry, in one of those realities, odds are one of the me’s developed a multiversal bomb that destroyed all the realities other than ours.
Where it gets strange is that there are actually an equal number of multiverse that have a version of you as there are that do not contain a version of you.
For the sake of simple math, let’s assume that there are an infinite number of multiverses and that the amount of those which contain a version of you is 1/10th.
So let’s take the amount of multiverses and divide them by ten. What do we get? Infinity.
It’s like trying to say there are fewer rational numbers between 1 and 2 than there are between 2 and 10. The number is always infinite.
No, there are some infinities bigger than other infinities. I know it sounds dumb, but this has been mathematically demonstrated. All infinities aren’t the same size, basically.
The set of rational numbers is larger than the set of integer numbers, even though they are both infinite.
What the person you replied is trying to say is that the intinite amount of universes that exist is infinitely larger that the infinite amount of universes in which you exist.
Personally, I think we can’t mathematically understand if the multiverse is a countable or uncountable infinite… Maybe we can? I don’t know.
https://philosophy.stackexchange.com/questions/12823/is-the-number-of-universes-finite-countably-infinite-or-uncountably-infinite-a